Viscous flow computations are required to predict the heat flux or the viscous drag on an hypersonic re-entry vehicle. When real gas effects are included, Navier–Stokes computations are very expensive, whereas the use of standard boundary layer approximations does not correctly account for the ‘entropy layer swallowing’ phenomenon. The purpose of this paper is to present an extension of a new boundary layer theory, called the ‘defect approach’, to two-dimensional hypersonic flows including chemical and vibrational non-equilibrium phenomena. This method ensures a smooth matching of the boundary layer with the inviscid solution in hypersonic flows with strong entropy gradients. A new set of first-order boundary layer equations has been derived, using a defect formulation in the viscous region together with a matched asymptotic expansions technique. These equations and the associated transport coefficient models as well as thermochemical models have been implemented. The prediction of the flow field around the blunt-cone wind tunnel model ELECTRE with non-equilibrium free-stream conditions has been done by solving first the inviscid flow equations and then the first-order defect boundary layer equations. The numerical simulations of the boundary layer flow were performed with catalytic and non-catalytic conditions for the chemistry and the vibrational mode. The comparison with Navier–Stokes computations shows good agreement. The wall heat flux predictions are compared to experimental measurements carried out during the MSTP campaign in the ONERA F4 wind tunnel facility. The defect approach improves the skin friction prediction in comparison with a classical boundary layer computation.